For non-custodial parents, IRS Form 8332 is required to claim the children as dependents.
The wording in the divorce decree will have no practical value without it.
It is critically important that any matters with tax implications (spousal support, child support, retirement plans, other income, deductions & credits etc.) be addressed in the Final Decree, together with the execution of any required documents. "Once it's done, it probably can't be undone."
Please call me if you have any questions regarding these or other tax-related issues, before anything is finalized.